Acta mathematica scientia,Series B

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EFFICIENT ESTIMATION OF FUNCTIONAL-COEFFICIENT REGRESSION MODELS WITH DIFFERENT SMOOTHING VARIABLES

Zhang Riquan; Li Guoying   

  1. 1.Department of Mathematics, Shanxi Datong University, Datong 037009, China; 2.Department of Statistics, East China Normal University, Shanghai 200062, China; 3.Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China
  • Received:2005-05-08 Revised:2006-10-29 Online:2008-10-20 Published:2008-10-20
  • Contact: Zhang Riquan

Abstract:

In this article, a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined. First step, by the local linear technique and the averaged method, the initial estimates of the coefficient functions are given. Second step, based on the initial estimates, the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure. The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions. Two simulated examples show that the procedure is effective.

Key words: Asymptotic normality, averaged method, different smoothing variables, functional-coefficient regression models, local linear method, one-step backfitting procedure

CLC Number: 

  • 62G08
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